Thread: Why do I keep getting this wrong?

The problem


3x-(1+2x)=6 Please pretend the parenthesis are aboslute value bars

my solution

divide both sides by -1




or

x= 1 or x=7, but only seven is valid in the original equation. Why?










Thank you in advance!

Originally Posted by Coach

The problem


3x-(1+2x)=6 Please pretend the parenthesis are aboslute value bars

my solution

divide both sides by -1




or

x= 1 or x=7, but only seven is valid in the original equation. Why?

Thank you in advance!

|1 + 2x| = 3x - 6.

Note that:
1. |1 + 2x| = 1 + 2x when 1 + 2x > 0 => x > -1/2.
2. |1 + 2x| = -(1 + 2x) = -1 - 2x when 1 + 2x < 0 => x < -1/2.

1. 1 + 2x = 3x - 6 AND x > -1/2 => x = 7 AND x > -1/2 => x = 7.

2. -1 - 2x = 3x - 6 AND x < -1/2 => x = 1 AND x < -1/2 => no solution.

So x = 7 is the only solution.